CN112819322A - Power transmission line path scheme evaluation method based on improved fuzzy analytic hierarchy process - Google Patents

Power transmission line path scheme evaluation method based on improved fuzzy analytic hierarchy process Download PDF

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CN112819322A
CN112819322A CN202110128082.8A CN202110128082A CN112819322A CN 112819322 A CN112819322 A CN 112819322A CN 202110128082 A CN202110128082 A CN 202110128082A CN 112819322 A CN112819322 A CN 112819322A
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黄勃
高云波
张承威
张贤
都伟杰
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Changzhou Changgong Electric Power Design Institute Co ltd
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Abstract

The invention discloses a power transmission line path scheme evaluation method based on an improved fuzzy analytic hierarchy process, which comprises the following steps of: s1: constructing an influence index set and a scheme set to be evaluated; s2: establishing a single influence index fuzzy evaluation matrix of a fuzzy relation after carrying out standardization processing on the influence index set; s3: constructing a judgment matrix for determining the weight of each influence index according to the fuzzy evaluation matrix, and optimally calculating the judgment matrix by adopting a particle swarm algorithm so as to obtain the weight value of each index; s4: and constructing a weight matrix by the weight values of the influence indexes, and solving a fuzzy comprehensive evaluation value of each scheme according to a fuzzy mathematical equation so as to obtain an optimal power transmission path scheme. The invention analyzes the advantages and disadvantages of the line path scheme by using the fuzzy theory, and optimizes the judgment matrix for determining each influence index by using the particle swarm optimization, so that the weight assignment of the influence indexes is more scientific and reasonable, thereby being beneficial to the evaluation and optimization of the scheme.

Description

Power transmission line path scheme evaluation method based on improved fuzzy analytic hierarchy process
Technical Field
The invention relates to the field of power transmission engineering design, in particular to a power transmission line path scheme evaluation method based on an improved fuzzy analytic hierarchy process.
Background
With the strong advocated 'new capital construction' of the national grid company, the construction strength of the transmission project is also increasing continuously. The design of the transmission line is the first link of the whole project, and the transmission line is a multi-face systematic work including path selection, tower positioning, electrical design and the like, wherein the path selection is the basis of the whole design work and is related to the manufacturing cost, construction and safety of the whole project. When the traditional manual mode is used for evaluating the power transmission line path, more influence indexes need to be considered, most of the influence indexes cannot be quantitatively described, the influence on the power transmission line is inconsistent, and the judgment can only be carried out by means of subjective experience of designers. With the development of computer technology and various optimization methods and the advantages of three-dimensional design technology in the aspect of information acquisition, scheme evaluation by means of manual experience alone cannot meet the requirement for optimization of a power transmission path scheme, so that various important indexes influencing power transmission line path selection need to be researched and analyzed, and the importance of each influencing index is comprehensively evaluated by establishing a mathematical model, so that the power transmission line path selection is more economical and reasonable, and scientific
The existing power transmission line path selection and evaluation methods can be mainly divided into two categories: based on subjective qualitative judgments and system logic analysis, respectively. The subjective qualitative judgment method mainly ranks and compares the influence indexes of all the influence path schemes according to expert knowledge, and the judgment of the subjective level mostly depends on experience, although expert theory is helpful to analysis to a certain extent, the scientificity and comprehensiveness of selection or evaluation results cannot be guaranteed. The system logic analysis mainly adopts an analytic hierarchy process, the analytic hierarchy process divides each influence index in the complex problem into mutually-connected ordered hierarchies, gives quantitative representation to the relative importance of each hierarchy, and determines the weight of the relative importance order of each element in each hierarchy by a mathematical method. Although the method is simple, practical and easy to operate, problems still exist, particularly when the judgment matrix does not have consistency, the reasonability of the weighted value calculated through the matrix is poor, and the matrix adjustment is tedious.
Therefore, the method combines the advantages of the traditional power transmission path scheme evaluation method based on the analytic hierarchy process, utilizes the particle swarm algorithm to check and correct the judgment matrix, and solves the problems that the weighted value is set in the evaluation process and is not fit with the data reality and the decision process lacks certain scientificity.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a transmission line path scheme evaluation method based on an improved fuzzy analytic hierarchy process, which can solve the defects in the prior art.
The technical scheme is as follows: the invention relates to a power transmission line path scheme evaluation method based on an improved fuzzy analytic hierarchy process, which comprises the following steps of:
s1: constructing an influence index set and a scheme set to be evaluated;
s2: establishing a single influence index fuzzy evaluation matrix of a fuzzy relation after carrying out standardization processing on the influence index set;
s3: constructing a judgment matrix for determining the weight of each influence index according to the fuzzy evaluation matrix, and optimally calculating the judgment matrix by adopting a particle swarm algorithm so as to obtain the weight value of each index;
s4: and constructing a weight matrix by the weight values of the influence indexes, and solving a fuzzy comprehensive evaluation value of each scheme according to a fuzzy mathematical equation so as to obtain an optimal power transmission path scheme.
Further, in step S1, the influence index set and the to-be-evaluated scheme set may be written as:
X＝(x1,x2,…xi…,xn) Formula (1);
Y＝(y1,y2,…yi…,ym) Formula (2);
in the formula (1), the element xiAnd representing various evaluation indexes influencing the selection of the power transmission line path scheme.
In the formula (2), the element yiRepresenting the jth scenario to be evaluated.
Further, in step S2, the fuzzy evaluation matrix is determined by:
s2.1: establishing a fuzzy mapping (function) of X corresponding to Y according to the corresponding relation between the influence indexes and the evaluation scheme: x → f (y), defining n influence indexes to constitute influence index sample set data of the whole m schemes as { X (i, j) | i ═ 1 to n, j ═ 1 to m }, and normalizing the sample set X (i, j), wherein the larger the value, the better the normalized processing formula of the type data is:
Figure BDA0002924144680000031
the formula for normalizing the data is as follows:
Figure BDA0002924144680000032
in the formulae (3) and (4), xmin(i) And xmax(i) Respectively the minimum value and the maximum value of the ith index in the scheme, wherein r (i, j) is the normalized influence index value, namely the relative membership value of the ith influence index in the jth scheme under the priority;
s2.2: fuzzy evaluation matrix R (R (i, j))n×mSpecifically, it is represented as:
Figure BDA0002924144680000041
in the formula (5), r (i, j) is rijDenotes an influence index xiFor scheme yjAnd degree of membership of
Figure BDA0002924144680000042
Further, in step S3, the determination matrix for determining each influence index weight and the calculation of each index weight based on the particle swarm algorithm are determined by the following method:
s3.1: the sample standard deviations s (i) for each impact index are introduced as:
Figure BDA0002924144680000043
s3.2: the structure of the judgment matrix is determined by the following method:
Figure BDA0002924144680000044
in the formula (7), sminAnd smaxMaximum and minimum values of { s (i) | i ═ 1 to n }, and relative importance degree parameter value am＝min{9,int[smax/smin+0.5]And the functions of taking a small function and taking an integer are min and int, respectively.
A is toikThe value of the element composition determination matrix a ═ aik}n×mIn addition, according to the definition of the judgment matrix A, there are
Figure BDA0002924144680000045
In formula (8) { wiI is 1 to n, and is a weight value of each influence index.
S3.3: the weighted value of each index obtained by optimally calculating the judgment matrix by adopting a particle swarm algorithm is determined by the following method:
let Y be { Yik}n×nThe weight value of each element of Y is still marked as { wiIf |, is 1 to n }, the Y matrix satisfying the minimum of equations (8) and (9) is a correction determination matrix of a:
Figure BDA0002924144680000051
Figure BDA0002924144680000052
in the formulas (9) and (10), the objective function rjv (n) is called as the modification judgment function; beta is a non-negative parameter and is selected within 0,0.3 according to experience.
In order to solve the nonlinear optimization problem of the formula (9), a particle swarm algorithm is adopted for solving, the optimization target is that an objective function RJV (n) is less than 0.1, and an optimization variable is a weighted value { w }iI is 1 to n and the correction determination matrix Y is { Y ═ Y }ik}n×nThe upper triangular matrix element of (1) is a group of n (n +1)/2 optimized variables, wherein each variable is used as a particle, and each particle is expressed as a D-dimensional vector and is recorded as:
Figure BDA0002924144680000053
the velocity of the ith particle is noted as:
Figure BDA0002924144680000054
taking the formula (9) as a fitness function of the particle swarm algorithm, substituting the initial particles into the fitness function to calculate to obtain the current optimal fitness value and the individual optimal solution pbestAnd colony optimal solution gbestThen, the ith particle updates the velocity and position according to equations (13-1) and (13-2):
Figure BDA0002924144680000055
Figure BDA0002924144680000056
in the formulas (13-1) and (13-2), d represents a dimension number; omega is an inertia factor and generally takes the value of 0.6; c. C1、c2The acceleration constant is generally 1.7; r is1、r2Is [0,1 ]]A random number in between; alpha is a speed constraint factor, and is generally 0.8; and k is the current iteration number.
After the speed and the position of each particle are updated, the optimal fitness value is obtained by calculation of the formula (9) again, and the individual optimal solution p is updatedbestAnd colony optimal solution gbestJudging whether the optimal fitness value meets a termination condition smaller than 0.1, and if so, finishing the optimization calculation; and if the optimal solution does not meet the end condition, updating the speed and the position of the particles again, calculating the optimal fitness value, and updating the individual and community optimal solution until the end condition is met. Finally, all the best individual solutions, namely the weight value { w }iI is 1 to n and the correction determination matrix Y is { Y ═ Y }ik}n×nUpper triangular matrix elements of (1).
Further, in step S4, the fuzzy comprehensive evaluation value and the optimal power transmission path plan are determined by:
s4.1: according to each influence index weighted value { w obtained in step S3.3iI | ═ 1 to n } constructs a weight matrix W:
W＝(w1,w2,…wi,…,wn) (14)；
in formula (14), the element wiIndicates an influence index xiA weight value defining a degree for each protocol involved in the comparison.
S4.2: and (3) according to a fuzzy mathematical equation W & R ═ Z, obtaining a comprehensive evaluation quality degree result Z of the scheme to be evaluated:
Figure BDA0002924144680000061
the fuzzy mathematical operation rule of equation (15) is:
Figure BDA0002924144680000062
in the formula (16), "Λ" represents a small value, and "V" represents a large value.
Each element in Z is a fuzzy comprehensive evaluation value Z (j), and the higher the fuzzy comprehensive evaluation value is, the better the scheme is. And selecting the scheme with the highest fuzzy comprehensive evaluation value as the optimal power transmission line path scheme.
Drawings
Fig. 1 is a calculation flowchart of the method for evaluating a transmission line path based on the improved fuzzy analytic hierarchy process according to the present invention.
Fig. 2 is a flowchart of a calculation of the judgment matrix and the index weight value based on particle swarm optimization in the embodiment of the present invention.
Detailed Description
The specific embodiment of the invention discloses a power transmission line path scheme evaluation method based on an improved fuzzy analytic hierarchy process, which comprises the following steps of:
s1: constructing an influence index set and a scheme set to be evaluated;
s2: establishing a single influence index fuzzy evaluation matrix of a fuzzy relation after carrying out standardization processing on the influence index set;
s3: constructing a judgment matrix for determining the weight of each influence index according to the fuzzy evaluation matrix, and optimally calculating the judgment matrix by adopting a particle swarm algorithm so as to obtain the weight value of each index;
s4: and constructing a weight matrix by the weight values of the influence indexes, and solving a fuzzy comprehensive evaluation value of each scheme according to a fuzzy mathematical equation so as to obtain an optimal power transmission path scheme.
In step S1, the influence index set and the to-be-evaluated scheme set may be written as:
X＝(x1,x2,…xi…,xn) Formula (1);
Y＝(y1,y2,…yi…,ym) Formula (2);
in the formula (1), the element xiAnd representing various evaluation indexes influencing the selection of the power transmission line path scheme.
In the formula (2), the element yiRepresenting the jth scenario to be evaluated.
In step S2, the blur evaluation matrix is determined by:
s2.1: establishing a fuzzy mapping (function) of X corresponding to Y according to the corresponding relation between the influence indexes and the evaluation scheme: x → f (y), defining n influence indexes to constitute influence index sample set data of the whole m schemes as { X (i, j) | i ═ 1 to n, j ═ 1 to m }, and normalizing the sample set X (i, j), wherein the larger the value, the better the normalized processing formula of the type data is:
Figure BDA0002924144680000081
the formula for normalizing the data is as follows:
Figure BDA0002924144680000082
in the formulae (3) and (4), xmin(i) And xmax(i) Respectively the minimum value and the maximum value of the ith index in the scheme, wherein r (i, j) is the normalized influence index value, namely the relative membership value of the ith influence index in the jth scheme under the priority;
s2.2: fuzzy evaluation matrix R (R (i, j))n×mSpecifically, it is represented as:
Figure BDA0002924144680000083
in the formula (5), r (i, j) is rijDenotes an influence index xiFor scheme yjAnd degree of membership of
Figure BDA0002924144680000084
In step S3, the determination matrix for determining each influence index weight and the calculation of each index weight based on the particle swarm algorithm are determined by the following method:
s3.1: the sample standard deviations s (i) for each impact index are introduced as:
Figure BDA0002924144680000091
s3.2: the structure of the judgment matrix is determined by the following method:
Figure BDA0002924144680000092
in the formula (7), sminAnd smaxMaximum and minimum values of { s (i) | i ═ 1 to n }, and relative importance degree parameter value am＝min{9,int[smax/smin+0.5]And the functions of taking a small function and taking an integer are min and int, respectively.
A is toikThe value of the element composition determination matrix a ═ aik}n×mIn addition, according to the definition of the judgment matrix A, there are
Figure BDA0002924144680000093
In formula (8) { wiI is 1 to n, and is a weight value of each influence index.
S3.3: the weighted value of each index obtained by optimally calculating the judgment matrix by adopting a particle swarm algorithm is determined by the following method:
let Y be { Yik}n×nThe weight value of each element of Y is still marked as { wiIf |, is 1 to n }, the Y matrix satisfying the minimum of equations (8) and (9) is a correction determination matrix of a:
Figure BDA0002924144680000094
Figure BDA0002924144680000101
in the formulas (9) and (10), the objective function rjv (n) is called as the modification judgment function; beta is a non-negative parameter and is selected within 0,0.3 according to experience.
Referring to FIG. 2, in order to solve the nonlinear optimization problem of the formula (9), a particle swarm algorithm is adopted to solve, the optimization target is to enable the target function RJV (n) to be less than 0.1, and the optimization variable is a weight value { w }iI is 1 to n and the correction determination matrix Y is { Y ═ Y }ik}n×nThe upper triangular matrix element of (1) is a group of n (n +1)/2 optimized variables, wherein each variable is used as a particle, and each particle is expressed as a D-dimensional vector and is recorded as:
Figure BDA0002924144680000102
the velocity of the ith particle is noted as:
Figure BDA0002924144680000103
taking the formula (9) as a fitness function of the particle swarm algorithm, substituting the initial particles into the fitness function to calculate to obtain the current optimal fitness value and the individual optimal solution pbestAnd colony optimal solution gbestThen, the ith particle updates the velocity and position according to equations (13-1) and (13-2):
Figure BDA0002924144680000104
Figure BDA0002924144680000105
in the formulas (13-1) and (13-2), d represents a dimension number;omega is an inertia factor and generally takes the value of 0.6; c. C1、c2The acceleration constant is generally 1.7; r is1、r2Is [0,1 ]]A random number in between; alpha is a speed constraint factor, and is generally 0.8; and k is the current iteration number.
After the speed and the position of each particle are updated, the optimal fitness value is obtained by calculation of the formula (9) again, and the individual optimal solution p is updatedbestAnd colony optimal solution gbestJudging whether the optimal fitness value meets a termination condition smaller than 0.1, and if so, finishing the optimization calculation; and if the optimal solution does not meet the end condition, updating the speed and the position of the particles again, calculating the optimal fitness value, and updating the individual and community optimal solution until the end condition is met. Finally, all the best individual solutions, namely the weight value { w }iI is 1 to n and the correction determination matrix Y is { Y ═ Y }ik}n×nUpper triangular matrix elements of (1).
In step S4, the fuzzy comprehensive evaluation value and the optimal power transmission path plan are determined by:
s4.1: according to each influence index weighted value { w obtained in step S3.3iI | ═ 1 to n } constructs a weight matrix W:
W＝(w1,w2,…wi,…,wn) (14)；
in formula (14), the element wiIndicates an influence index xiA weight value defining a degree for each protocol involved in the comparison.
S4.2: and (3) according to a fuzzy mathematical equation W & R ═ Z, obtaining a comprehensive evaluation quality degree result Z of the scheme to be evaluated:
Figure BDA0002924144680000111
the fuzzy mathematical operation rule of equation (15) is:
Figure BDA0002924144680000112
in the formula (16), "Λ" represents a small value, and "V" represents a large value.
Each element in Z is a fuzzy comprehensive evaluation value Z (j), and the higher the fuzzy comprehensive evaluation value is, the better the scheme is. And selecting the scheme with the highest fuzzy comprehensive evaluation value as the optimal power transmission line path scheme.

Claims (10)

1. A method for evaluating a transmission line path, comprising:
constructing an influence index set and a scheme set to be evaluated;
establishing a single influence index fuzzy evaluation matrix of a fuzzy relation;
acquiring the weight value of each influence index;
constructing a weight matrix; and
and acquiring a fuzzy comprehensive evaluation value of each scheme to be evaluated, namely acquiring the power transmission line path.
2. The evaluation method according to claim 1,
the set of influence indicators is
X＝(x1,x2,…xi…,xn) Formula (1);
the set of solutions to be evaluated is
Y＝(y1,y2,…yi…,ym) Formula (2);
xii-th influence indicator, y, representing transmission line pathiRepresenting the ith scheme to be evaluated.
3. The evaluation method according to claim 1,
the establishing of the single influence index fuzzy evaluation matrix of the fuzzy relation comprises the following steps:
establishing fuzzy mapping (function) of X corresponding to Y according to the corresponding relation between the influence indexes and the evaluation scheme, namely X → F (Y);
defining n influence indexes to form an influence index sample data set of m schemes to be evaluated as { x (i, j) | i ═ 1-n, j ═ 1-m }, and carrying out standardization processing on the sample data set x (i, j) to obtain a standardized influence index value x (i, j);
taking the R (i, j) value as the element composition single influence index fuzzy evaluation matrix R ═ R (i, j)n×mI.e. by
Figure FDA0002924144670000021
r (i, j) is rijDenotes an influence index xiScheme to be evaluated yjAnd satisfies the condition that r is more than or equal to 0ij≤1,
Figure FDA0002924144670000022
4. The evaluation method according to claim 3,
the normalizing the sample data set x (i, j) comprises:
the larger the value, the better the type data is normalized by the formula
Figure FDA0002924144670000023
The smaller the value, the better the type data is normalized by the formula
Figure FDA0002924144670000024
xmin(i) Is the minimum value of the i-th influence index, xmax(i) And r (i, j) is a normalized influence index value, namely a relative membership value of the ith influence index belonging to the superior in the jth scheme to be evaluated.
5. The evaluation method according to claim 1,
the obtaining of the weight value of each influence index includes:
constructing a judgment matrix according to the fuzzy evaluation matrix;
and optimally calculating the judgment matrix by adopting a particle swarm algorithm to obtain the weight value of each influence index.
6. The evaluation method according to claim 5, wherein:
the constructing a judgment matrix according to the fuzzy evaluation matrix comprises:
sample standard deviations s (i) of the respective impact indicators are introduced, i.e.
Figure FDA0002924144670000031
Constructing a decision matrix, i.e.
Figure FDA0002924144670000032
A is toikThe value of the element composition determination matrix a ═ aik}n×mAnd is and
Figure FDA0002924144670000033
wherein
sminIs the minimum value of { s (i) | i ═ 1 to n }, smaxIs the maximum value of { s (i) | i ═ 1 to n }, the relative importance degree parameter value am＝min{9,int[smax/smin+0.5]The min and the int are a small function and an integer function respectively;
{wii is 1 to n, and is a weight value of each influence index.
7. The evaluation method according to claim 6,
the optimizing, calculating and judging matrix by adopting the particle swarm algorithm comprises the following steps:
setting a correction determination matrix, i.e. setting the correction determination matrix of a as Y ═ Yik}n×nThe weight value of each element of Y is still marked as { wiIf |, i is 1 to n }, the Y matrix satisfying the minimum of equations (8) and (9) is a correction determination matrix of a, that is, a matrix satisfying the minimum of equations (8) and (9) is a correction determination matrix of a
Figure FDA0002924144670000034
Figure FDA0002924144670000041
Optimizing variables by adopting a particle swarm algorithm, namely solving a formula (9) by adopting the particle swarm algorithm, wherein the optimization target is that an objective function RJV (n) is less than 0.1, and the optimization variables are weighted values { w }iI is 1 to n and the correction determination matrix Y is { Y ═ Y }ik}n×nThe upper triangular matrix element of (2) is n (n +1)/2 optimization variables in total; wherein
The target function RJV (n) is a correction judgment function, beta is a non-negative parameter and is selected within [0,0.3 ].
8. The evaluation method according to claim 7,
the particle swarm optimization variables comprise:
obtaining the current optimal fitness value and the individual optimal solution pbestAnd colony optimal solution gbestI.e. by
Forming a community M by n (n +1)/2 variables, wherein each variable is taken as a particle, each particle is expressed as a D-dimensional vector and is recorded as a D-dimensional vector
Figure FDA0002924144670000042
The velocity of the ith particle is recorded as
Figure FDA0002924144670000043
Taking the formula (9) as a fitness function of the particle swarm algorithm, substituting the initial particles into the fitness function for calculation to obtain the current optimal fitness value and the individual optimal solution pbestAnd colony optimal solution gbest；
The speed and position of the particle are updated, i.e. the speed and position are updated according to the formula (13-1) and (13-2) for the ith particle,
Figure FDA0002924144670000044
Figure FDA0002924144670000045
updating individual optimal solutions pbestAnd colony optimal solution gbestAfter the speed and the position of each particle are updated, replacing the formula (9) again to calculate to obtain an optimal fitness value;
determine whether the optimal fitness value satisfies a termination condition of less than 0.1, i.e.
If so, finishing the optimization calculation; if the optimal solution meets the termination condition, the speed and the position of the particles are updated again, the optimal fitness value is calculated, and the individual and community optimal solution is updated until the termination condition is met;
output all optimal individual solutions, i.e. weight values wiI is 1 to n and the correction determination matrix Y is { Y ═ Y }ik}n×nUpper triangular matrix elements of (1); wherein
d represents the dimension number, omega is the inertia factor, c1、c2Is an acceleration constant, r1、r2Is [0,1 ]]And (4) a random number in between, wherein alpha is a speed constraint factor, and k is the current iteration number.
9. The evaluation method according to claim 7,
the acquiring of the fuzzy comprehensive evaluation value of each scheme to be evaluated comprises the following steps:
according to each influence index weighted value { wiI 1 to n, a weight matrix W is constructed, i.e.
W＝(w1,w2,…wi,…,wn) Formula (14);
according to the fuzzy mathematical equation W.R ═ Z, the result Z of the comprehensive evaluation quality degree of the scheme to be evaluated is obtained, namely
Figure FDA0002924144670000051
Wherein
wiIndicates an influence index xiAnd defining the weight value of each scheme to be evaluated participating in comparison.
10. The evaluation method according to claim 9,
the fuzzy mathematics operation rule is as follows:
Figure FDA0002924144670000061
wherein
"Λ" means taking a small value, and "v" means taking a large value;
each element in Z is a fuzzy comprehensive evaluation value Z (j).
CN202110128082.8A 2021-01-29 2021-01-29 Power transmission line path scheme evaluation method based on improved fuzzy analytic hierarchy process Pending CN112819322A (en)

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CN113780653A (en) * 2021-09-07 2021-12-10 上海电力大学 Power transmission line path scheme optimization method based on cloud matter elements
CN114036452A (en) * 2021-11-11 2022-02-11 中国电子科技集团公司第二十九研究所 Capacity evaluation method applied to discrete production line
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